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Magazine Problem 43
Solve each system of equations for real values of \(x\) and \(y.\) $$ \left\\{\begin{array}{l} y=x^{2}-4 \\ x^{2}-y^{2}=-16 \end{array}\right. $$
Problem 43
Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, ellipses, and hyperbolas. $$ 9 x^{2}-49 y^{2}=441 $$
Problem 44
Graph each equation of a parabola. Give the coordinates of the vertex. $$ x=2 y^{2} $$
Problem 44
Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, ellipses, and hyperbolas. $$ 25 y^{2}-16 x^{2}=400 $$
Problem 44
Solve each system of equations for real values of \(x\) and \(y.\) $$ \left\\{\begin{array}{l} y-x=0 \\ 4 x^{2}+y^{2}=10 \end{array}\right. $$
Problem 45
Graph each equation of a parabola. Give the coordinates of the vertex. $$ x=2(y+1)^{2}+3 $$
Problem 45
Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, ellipses, and hyperbolas. $$ 4(x+1)^{2}+9(y+1)^{2}=36 $$
Problem 45
Solve each system of equations for real values of \(x\) and \(y.\) $$ \left\\{\begin{array}{l} 3 y^{2}=x y \\ 2 x^{2}+x y-84=0 \end{array}\right. $$
Problem 46
Solve each system of equations for real values of \(x\) and \(y.\) $$ \left\\{\begin{array}{l} x^{2}+y^{2}=10 \\ 2 x^{2}-3 y^{2}=5 \end{array}\right. $$
Problem 46
Write each equation in standard form, if it is not already so, and graph it. The problems include equations that describe circles, parabolas, ellipses, and hyperbolas. $$ 16 x^{2}+25(y-3)^{2}=400 $$
